3

Part of 2011 South africa National Olympiad

Problems(1)

SAMO 2011 Senior Round 3 Problem 3

Source:

We call a sequence of

m

consecutive integers a friendly sequence if its first term is divisible by

1

, the second by

2

(m-1)^{th}

m-1

, and in addition, the last term is divisible by

m^2

Does a friendly sequence exist for (a)

m=20

m=11

number theoryleast common multiplemodular arithmetic